Investigation of a New Post Punching Through an Existing Concrete Slab
A Conversation in Structural Concrete
Background
So, the question has been raised, " ... what about a plain concrete slab?" Recall that last time (here) we were looking at the situation of seeing if an existing concrete slab on grade would be suitable for supporting a new post. In that example the slab was a `reinforced' concrete slab. What if it is plain (concrete)? Well, let's look at it. We will use the Strength Design (SD) approach.
Strength Design Example
FACTORED LOAD
Recall that our factored load is ... (from before)
Pu = 1.2 (900 lb) + 1.6 (2100 lb) = 4440 lb = Vu.
FACTORED STRENGTH
The punching shear strength of plain concrete is taken to be different than the strength of the concrete (alone) in reinforced concrete; it is less, in fact, much less.
... Vn = nominal (`perfect world') strength of plain concrete in punching shear = ...
... (8/3) bo h √f'c,
where,
bo is the perimeter of a vertical equivalent shearing plane a distance h/2 from the faces of the post, and
h = the thickness of the slab, taken to be the actual thickness minus 2 in. where the slab is cast against earth.
The strength reduction factor is also different ... for plain concrete ... φ = 0.55.
In this case the `h' is the same as the d from before; and so the same with bo. Other things equal (except that the slab is not reinforced) ...
... the factored punching shear strength is ... (and 8/3 = 2.67)
... φ Vn = φ 2.67 bo h √f'c = 0.55 (8/3) 22 in. (2 in.) √2500 psi = 3227 lb.
Whoa, ... is Vu = 4440 lb ≤ φ Vn = 3227 lb? No! ... NOT GOOD.
In terms of a `unity check' ...
Is Vu / φ Vn = 4440 lb / 3227 lb = 1.34 ≤ 1.00? ... NO!
By considering plain concrete the factored strength is about half that of reinforced concrete. And note that the reinforcement considered was not shear reinforcement, it was just reinforcement (probably temperature-shrinkage reinforcement).
For plain concrete we must use a more `brutal' strength reduction factor, and is likewise taken to have a lesser nominal strength.
Options
As is, the situation is not good. What are our options? Well, a base of some kind that spreads the load out would be an option. Another option would be to cut the slab and install an appropriate (new) footing for the post.
References
Post Punching Through a Concrete Slab, Jeff Filler, Associated Content.
Building Code Requirements for Structural Concrete, ACI 318, American Concrete Institute, P.O. Box 9094, Farmington hills, Michigan, 48333.
Published by Jeff Filler
Consulting Engineer, Educator, Aspiring Writer and Photographer, Husband, Father, and Serious Hunter. View profile
Strength of a Reinforced Concrete BeamLesson illustrates the strength and safety provided by using reinforcement in a previously considered plain concrete beam. 
Punching ShearLesson describes common cases of potential punching shear in structural concrete design and how to deal with them.
Punching Shear Example 1Example illustrates some assumptions and calculations involved in the evaluation of an existing slab on grade for supporting a (new) concentrated load.
Punching Shear Example 2Example showing beam shear and punching shear calculations for a footing resisting a concentrated load from a column. - Beam Shear in Reinforced Concrete - RevisedLesson provides basic equations for shear strength in reinforced concrete with example calculations.
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2 Comments
Post a CommentI don't think I understand your comment unless you mean the bearing capacity of the `soil' below the post. In that case - that's a very good question. My take on this - is that for something like a post punching through a relatively large slab (basement slab or patio slab, as opposed to slab footing), the concrete will have to crack to significantly load the soil. (The slab will be way less flexible than the soil.) BUT, cracking the slab is the very thing we are needing to avoid.
Jeff - this doesn't seem to deduct for the bearing capacity of the slab directly below the post - this does not require shear transfer.
I haven't looked close enough but the perimeter in unreinforced concrete might conservatively be the size of the post, while in reinforced concrete it is d/2 on all sides of the post. These changes might make the unreinforced slab adequate.